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Motivated by recent experiments on the Kitaev honeycomb magnet $alphatext{-RuCl}_3$, we introduce time-domain probes of the edge and quasiparticle content of non-Abelian spin liquids. Our scheme exploits ancillary quantum spins that communicate via time-dependent tunneling of energy into and out of the spin liquids chiral Majorana edge state. We show that the ancillary-spin dynamics reveals the edge-state velocity and, in suitable geometries, detects individual non-Abelian anyons and emergent fermions via a time-domain counterpart of quantum-Hall anyon interferometry. We anticipate applications to a wide variety of topological phases in solid-state and cold-atoms settings.
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The S=3/2 Kitaev honeycomb model (KHM) has defied an analytical as well as numerical understanding because it is not exactly soluble like its S=1/2 brethren and in contrast to other spin-S Kitaev models numerical methods are plagued by a massive pile up of low energy states. Here, we uncover the phase diagram of the S=3/2 KHM and find gapped and gapless quantum spin liquids (QSLs) generally coexisting with spin quadrupolar orders. Employing an SO(6) Majorana fermion representation of spin-3/2s, we find an exact representation of the conserved plaquette fluxes in terms of static Z$_2$ gauge fields akin to the S=1/2 KHM which enables us to treat the remaining interacting matter fermion sector in a parton mean-field theory. The latter provides an explanation for the extensive near degeneracy of low energy states in the gapless phase via the appearance of almost flat Majorana bands close to zero energy. Our parton description is in remarkable quantitative agreement with numerical simulations using the density matrix renormalization group method, and is furthermore corroborated by the addition of a single ion anisotropy which continuously connects the gapless Dirac QSL of our model with that of the S=1/2 KHM. We discuss the implications of our findings for materials realization of higher S=3/2 KHMs and the stability of the QSL phase with respect to additional interactions.
The Kitaev spin liquid provides a rare example of well-established quantum spin liquids in more than one dimension. It is obtained as the exact ground state of the Kitaev spin model with bond-dependent anisotropic interactions. The peculiar interactions can be yielded by the synergy of spin-orbit coupling and electron correlations for specific electron configuration and lattice geometry, which is known as the Jackeli-Khaliullin mechanism. Based on this mechanism, there has been a fierce race for the materialization of the Kitaev spin liquid over the last decade, but the candidates have been still limited mostly to $4d$- and $5d$-electron compounds including cations with the low-spin $d^5$ electron configuration, such as Ir$^{4+}$ and Ru$^{3+}$. Here we discuss recent efforts to extend the material perspective beyond the Jackeli-Khaliullin mechanism, by carefully reexamining the two requisites, formation of the $j_{rm eff}=1/2$ doublet and quantum interference between the exchange processes, for not only $d$- but also $f$-electron systems. We present three examples: the systems including Co$^{2+}$ and Ni$^{3+}$ with the high-spin $d^7$ electron configuration, Pr$^{4+}$ with the $f^1$-electron configuration, and polar asymmetry in the lattice structure. In particular, the latter two are intriguing since they may realize the antiferromagnetic Kitaev interactions, in contrast to the ferromagnetic ones in the existing candidates. This partial overview would stimulate further material exploration of the Kitaev spin liquids and its topological properties due to fractional excitations.
We investigate the generic features of the low energy dynamical spin structure factor of the Kitaev honeycomb quantum spin liquid perturbed away from its exact soluble limit by generic symmetry-allowed exchange couplings. We find that the spin gap persists in the Kitaev-Heisenberg model, but generally vanishes provided more generic symmetry-allowed interactions exist. We formulate the generic expansion of the spin operator in terms of fractionalized Majorana fermion operators according to the symmetry enriched topological order of the Kitaev spin liquid, described by its projective symmetry group. The dynamical spin structure factor displays power-law scaling bounded by Dirac cones in the vicinity of the $Gamma$, $K$ and $K$ points of the Brillouin zone, rather than the spin gap found for the exactly soluble point.
We theoretically study THz-light-driven high-harmonic generation (HHG) in the spin-liquid states of the Kitaev honeycomb model with a magnetostriction coupling between spin and electric polarization. To compute the HHG spectra, we numerically solve the Lindblad equation, taking account of the dissipation effect. We find that isotropic Kitaev models possess a dynamical symmetry, which is broken by a static electric field, analogous to HHG in electron systems. We show that the HHG spectra exhibit characteristic continua of Majorana fermion excitations, and their broad peaks can be controlled by applying static electric or magnetic fields. In particular, the magnetic-field dependence of the HHG spectra drastically differs from those of usual ordered magnets. These results indicate that an intense THz laser provides a powerful tool to observe dynamic features of quantum spin liquids.
We study the excitation spectrum of the spin-1 Kitaev model using the symmetric tensor network. By evaluating the virtual order parameters defined on the virtual Hilbert space in the tensor network formalism, we confirm the ground state is in a $mathbb{Z}_2$ spin liquid phase. Using the correspondence between the transfer matrix spectrum and low-lying excitations, we find that contrary to the dispersive Majorana excitation in the spin-1/2 case, the isotropic spin-1 Kitaev model has a dispersive charge anyon excitation. Bottom of the gapped single-particle charge excitations are found at $mathbf{K}, mathbf{K}=(pm2pi/3, mp 2pi/3)$, with a corresponding correlation length of $xi approx 6.7$ unit cells. The lower edge of the two-particle continuum, which is closely related to the dynamical structure factor measured in inelastic neutron scattering experiments, is obtained by extracting the excitations in the vacuum superselection sector in the anyon theory language
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